At the opening ceremony of the One Young World Summit in Bogota, Colombia, Geldof turned his particular attention to Aung San Suu Kyi over her government's treatment of the Rohingya minority in Myanmar.
"On this stage are some of the greatest people who have fought for justice and peace and equality in our world," he said, referring to the Nobel Peace Laureates sitting on stage behind him.
"And one of their number in Myanmar insults them - insults them all. Who took the greatest prize that humans can give to another and then becomes one of the great ethnic cleansers of our planet. This is a disgrace."
Ms Suu Kyi, who won the Nobel Peace Prize in 1991, spent a total of 15 years under house arrest when in opposition.
However, she has drawn widespread criticism for her silence on the treatment of the Rohingya people, which UN human rights chief Zeid Ra'ad Al Hussein called "a textbook example of ethnic cleansing".
Geldof was joined on stage by counsellors from the One Young World Conference, including former UN secretary-general Kofi Annan, and Colombia's President Juan Manuel Santos, to open the three-day summit.
The summit, in its seventh year, brings together notable young people from 194 countries to discuss issues including climate change, conflict resolution and economic development.
"I loathe these people. I despise these people. How dare they behave in the manner they behave. How dare they daily insult us as human beings."
Geldof did give praise to Mr Santos and his efforts to bring peace to Colombia.